Prediction of the Residual Stiffness of Composite Materials under Random Vibration Loading Using a Combined Probabilistic Random Forest and Probabilistic Stiffness Model

The residual stiffness distribution of fiber-reinforced polymer (FRP) is an essential basis for evaluating structural fatigue reliability. This paper proposes a combined random forest and probability model for evaluating and predicting residual stiffness in FRP laminates subjected to random vibration loads. The first phase of stiffness degeneration is predicted through the random forest, and the second phase of stiffness degeneration is predicted by the probability model. Considering the randomness of the load and the dispersion of composite materials, the model of residual stiffness based on the normal distribution for FRP laminates is derived by combining residual stiffness with probability density. The validity of the model is verified by static strength test data and fatigue life test data of glass fiber–reinforced polymer (GFRP) and carbon fiber–reinforced polymer (CFRP). The average errors in the predicted stiffness results are within 5%. Furthermore, the model outputs a residual stiffness probability distribution, which provides the likelihood of each prediction. This distribution accounts for uncertainties associated with single-point prediction, and the true residual stiffness mainly lies within the 95% confidence interval of the distribution. As a result, the model is accurate and dependable in predicting the residual stiffness of composites under random vibration loading.